One of the main goals of the near-field scanning microwave microscopy is to quantitatively measure a material's complex microwave permittivity (dielectric constant and conductivity) with high sensitivity of lateral and/or depth selectivity (i.e. to determine the material's property over a small volume while ignoring the contribution of that volume's surrounding environment). This is particularly important in measurements on complex structures, such as semiconductor devices or composite materials, where, for example, the permittivity of one line or layer must be determined without having knowledge of the properties of the neighboring lines or underlying layers.
In order to perform highly localized quantitative measurements of a material's complex permittivity at microwave frequencies by means of near-field microwave microscopy the near-field probe requires calibration. All calibration procedures currently in use for near-field microwave microscopy employ some information about the actual tip geometry which would include, for example, the tip curvature radius, etc., and further requires knowledge of the absolute tip-to-sample separation as presented, for example, in C. Gao, et al., Rev. Scientific Instruments, 69, 3846, 1998.
If there is no radiation from the tip of the probe, the response of the electrical near-field probe depends on the fringe impedance of the tip Zt=1/iωCt, where Ct is the static capacitance of the tip of the probe. This capacitance depends on the physical geometry of the tip, the tip-to-sample separation d, and the sample's dielectric constant ∈r (assuming the sample is uniform in shape). Thus, in order to extract the sample's dielectric constant ∈r from the impedance of the tip Zt, the tip geometry and absolute tip-to-sample separation must be known to a high degree of accuracy.
However, accurate determination of these parameters is difficult and often impractical, especially for very small tips of less than or on the order of a few microns in size which are of great importance for near-field microwave microscopy. Further, analytical solutions to the problem of interaction between a near-field tip and a sample exist only for the most simple tip geometries, such as a sphere or a flush end of a coaxial line (W. R. Smythe, Static and Dynamic Electricity, McGraw-Hill, NY, 1968; J. Baker-Javis, et al., IEEE Trans. Instrumentation and Measurement, 43, 711, 1994).
It is therefore highly desirable to perform quantitative measurement of a material's dielectric constant which does not require knowledge of either the actual tip geometry or the absolute tip-to-sample separation.
In microwave microscopy the basic measurement is a determination of the reflection of a microwave signal from a probe positioned in close proximity to a sample. Phase and amplitude of the reflected signal may be determined directly by using a vector network analyzer or by determination of the resonant frequency and quality factor of a resonator coupled to the probe.
Thus, determination of the resonant frequency and quality factor of a resonator coupled to the probe is extremely important to develop overall measurements of the material complex permittivity. The most conventional way of measuring the resonant frequency and quality factor of a microwave resonator is through analyzing the complex reflection (S11) or transmission (S21) coefficient of the resonator as a function of frequency measured with a vector network analyzer. A comprehensive review of such methods has been made by P. J. Peterson and S. M. Anlage in Journal of Applied Physics, 84, 3392, 1998. In particular, it has been found that the most precise and robust method is the phase vs. frequency fit, which provides precision in the resonant frequency about 1×10−8 and approximately 3×10−10 for the signal-to-noise ratios (SNR) ˜49 and ˜368, respectively when the data is averaged over 75 traces for a resonator with a Q-factor ˜106.
Some applications involving the use of a resonator, require substantially precise simultaneous and fast measurements. This is important in scanning near-field microwave microscopy (NFMM) where the probe resonant frequency and Q-factor must often be quickly acquired during the scan. For most scanning applications, the desirable sampling time is on the order of or less than 1 second per point. Though precise, the methods described in Peterson, et al., are relatively slow, since the total averaging time is on the order of or greater than 10 seconds assuming that at least 100 ms is required by the vector network analyzer (NWA) to acquire a single S parameter vs. frequency trace. Moreover, it is likely that the resonant frequency is not going to be as stable as 10−8 or 10−10 during this period of time.
The existing methods for the resonant frequency and Q-factor measurements in the NFMM are generally deficient for the following reasons. Conventional S11 or S21 measurement using the NWA are slow. Amplitude measurement at a fixed frequency (M. Tabib-Azar, et al., Rev. Scientific Instruments 70, 2783, 1999) may be performed with the synthesized source, however, this method results in a convolution of the two resonator characteristics, such as resonant frequency and Q-factor. Frequency following techniques described in D. E. Steinhauer, et al., Applied Physics Letters, 71, 1736, 1997, are very fast (typical sampling rate is approximately 30 Hz), but neither precise nor accurate since the microwave source has to be used in the non-synthesized regime in order to lock a feedback loop. Distance following techniques described in F. Duewer, et al., Applied Physics Letters, 74, 2696, 1999, employ continuous adjustment of the probe-to-sample separation in a manner where the resonant frequency of the probe is maintained constant. Since this technique employs the synthesized source, it is fast and precise, however, the data obtained is generally a convolution of the sample topography and microwave properties.
Therefore, a novel approach to measurement of the resonant frequency, which is accurate, precise, and fast is needed to obtain a material's complex permittivity measurements with the use of near-field microwave probes.
A novel technique which permits performing measurements without knowledge of either the actual tip geometry or the absolute tip-to-sample separation to provide extra precise measurements of the frequency shift of the near-field probe is needed in the field of quantitative measurements of material's microwave properties.